Open API v2.0 Specification
ServiceStack implements the OpenAPI v2.0 Specification in its Open API Feature which you can install from NuGet with:
PM> Install-Package ServiceStack.Api.OpenApi
Then register in your AppHost with:
Plugins.Add(new OpenApiFeature());
When enabled you can access the Open API spec for your services at the /openapi endpoint. This is what the /swagger-ui/ uses to generate its dynamic UI for your Services.
Generating REST Client using Open API Spec
Which you can also use with Azure's AutoRest client to generate an AutoRest client from the spec.
But I don't see what the Swagger/OpenAPI Spec has to do with SoapUI? Soap Web Services are described and can have their clients generated from a WSDL, not the Open API spec.
SOAP Support
ServiceStack's SOAP Support also generates the WSDL for your Services which you can find linked on your Metadata Page.
Older Swagger 1.2 Spec
Alternatively ServiceStack also supports the older Swagger 1.2 Spec with its Swagger Feature which you can install from NuGet with:
PM> Install-Package ServiceStack.Api.Swagger
Then register in your AppHost with:
Plugins.Add(new SwaggerFeature());